Case Study 2: Piezoelectric Circular Plate

Transcription

1 Case Study 2: Piezoelectric Circular Plate PROBLEM - 3D Circular Plate, kp Mode, PZT4, D=50mm x h=1mm GOAL Evaluate the operation of a piezoelectric circular plate having electrodes in the top and bottom surfaces and polarized in the thickness mode. The operation is evaluated in the transversal (Radial) direction, i.e. kp mode. The size of the circular plate is 50mm diameter x 1mm thickness. The piezoelectric plate is made of PZT4 material. u r E h=1mm z y x P D=50mm Figure C2.1. Menu sequence for creating a circle D = 50 mm H = 1 mm Material: PZT4 Top and Bottom Electrodes Thickness Polarization

2 GEOMETRY/DRAWING 1. Start GiD Start GID using the desktop icon. Note: This example will incorporate both the menu and icon options to begin and transition to the most straightforward method as the example progresses. Later examples will outline the process and allow the user to select the method they are most comfortable with. All new processes will explain both options when introduced. 2. Create the 3D Model 2.1 Create the circle/surface Alternative 1: Using the Drop Down menus. Geometry Create Object Circle Enter center point 0,0 Enter Enter Normal Select then OK Enter Radius 25 Enter This sequence is illustrated in Figure C2.2. Figure C2.2. Menu sequence for creating a circle

3 Alternative 2: Using the Icons To create the circle using the icons bar, Click, the object icon drop menu will appear. Then click the circle icon. In the dialog box, enter the center for the circle (0,0) and press Enter. Then, enter a normal for the circle. In our case, choose Positive Z. Finally, enter the radius for the circle in the dialog box (25) and press Enter to finish the circle generation. This sequence is illustrated in Fig C2.3. Object Circle Circle Line (blue) Circle Surface (magenta) Figure C2.3. Icon sequence for creating a circle. The circle line (in blue) has been created with the corresponding surface (in magenta color). In this case, to allow quadrilateral meshing in the center of the disc, it is required to create an additional surface in the center are of the disc. This will be done later on. Since two surfaces will be created, the first thing is to remove the surface created for the disc and then created the needed new surface in the center. 2.2 Deleting the Surface Note: As indicated, this step is necessary before creating a quadrilateral element in the center for better meshing. Failure to delete this surface will cause issues later because of overlapping surfaces. Alternative 1: Delete Surface Using the Drop Down Menus Geometry Delete Surfaces Select Circle Surface ESC The process of deleting a surface using the drop down menu illustrated in Figure C2.4.

4 Select the surface to Delete (it will change the color to red) Delete Surface Once selected click "ESC" The surface has been removed Figure C2.4. (Left) Menu sequence for deleting a surface; (Right) Result after removing the surface. Only the circle line remains. Alternative 2: Delete Surface Using the Icons To remove the surface using the icons, Click. The delete drop menu will appear. Choose the surface icon,, to remove only the surface. Then, select Circle Surface to be removed. The surface will be highlighted in red. Press ESC to remove the surface. This sequence is shown in Figure C2.5. Delete Surface Select the surface to Delete (it will change the color to red) Once selected click "ESC" Figure C2.5. Icon sequence for deleting a surface The surface has been removed

5 2.3 Creating the center quadrilateral element for meshing of the center As indicated, to obtain a better mesh, a quadrilateral element will be created at the center of the circle. Alternative 1: Using the Drop Down Menus Geometry Create Straight line Points (0,5) Enter Points (5,0) Enter Points (0,-5) Enter Points (-5,0) Enter Points (0,5) Enter Join ESC. This sequence is shown in Figure C2.6. Introduce the coordinates of the new surface Figure C2.6. Menu sequence for creating the quadrilateral Alternative 2: Using the Icons Click Points (0,5) Enter Points (5,0) Enter Points (0,-5) Enter Points (-5,0) Enter Points (0,5) Enter Join ESC. This sequence is shown in Figure C2.7. Figure C2.7. Icon sequence for creating the quadrilateral

6 2.4 Dividing the circle The corners of the quadrilateral (square) need to be connected to the circle. The coordinates of the square were created to lie on the axis of the circle. Dividing the circle using the divide function will place a point on the each axis. This sequence is shown in Figure C2.8. The result is shown in Figure C2.9. Alternative 1: Using the Drop Down Menus Click Geometry Edit Divide Lines Num divisions Enter (4) OK This sequence can be seen in Figure C2.8. Alternative 2: Using the Icons Click. Then enter the number of divisions. Enter (4). Press OK to finish. This sequence can be seen in Figure C2.8. Figure C2.8. Sequence for dividing a line using drop down menus (left) and icons (right) Figure C2.9. The divided circle with a quadrilateral at the center

7 2.5 Creating Connecting lines The connecting lines need to be created from the corners of the quadrilateral to the points created on the circle. Both the menu and icon sequence are shown in the top panels of Figure C2.10. The first line and the final geometry are shown in the bottom panels of Figure C2.10. Alternative 1: Using the Drop Down Menus Click Geometry Create Straight line Control-A Select 1 st 2 - points ESC Select 2 nd 2 - points ESC Select 3 rd 2 - points ESC Select 4 th 2 - points ESC ESC This sequence can be seen in Figure C2.10 -top left. Alternative 2: Using the Icons Click Control-A Select 1 st 2 - points ESC Select 2 nd 2 - points ESC Select 3 rd 2 - points ESC Select 4 th 2 - points ESC ESC. See Figure C2.10 top right. Top Drop Menu Vertical Icons Bar Figure C2.10. Connecting the quadrilateral to the circle using the menus

8 2.6 Create surface Alternative 1: Using the Drop Down Menus GID will create surfaces automatically based on the information entered. Click Geometry Create NURBS surface Automatic Enter (4) OK This sequence is shown in Figure C2.11. The resultant surfaces are shown in Figure C2.12. Alternative 2: Using the Icons Figure C2.11. Menu sequence for creating surfaces The icon option requires that the bounding lines of the surface be selected to create the surface. This allows the user control over how the surfaces are created. Select the bounding entities that will form the edges of the surface, when finished with that surface click ESC. The cursor will remain for the creation of additional surfaces. The resultant surfaces are shown in Figure C2.12. Click ( ) Select the bounding lines of the first surface ESC Select the 2 nd set of bounding lines for the next surface ESC Repeat the same for the rest of surfaces ESC to quit. Figure C2.12. Geometry after the creation of surfaces

9 2.7 Create Volumes Using Copy and Create Alternative 1: Using the Drop Down Menus Utilities Copy Surfaces Translate Enter first point 0,0,0 Enter second point 0,0,1.0 Do Extrude: Volumes Select Finish In Case 1 the volume was created directly when the 2D geometry was extruded into 3D. This is usually the fastest way. This example will use a second method that creates the 3D geometry then the volumes to show an alternative method of volume creation. Click Utilities Copy. In the Copy menu, select Entities type: Surfaces and Translation for the type of Transformation. For this example, the First Point coordinate is the default value, i.e (0,0,0), the Second Point is the thickness of the plate, in this example 1mm, i.e. the Second Point should be (0,0,1.0). Check the box - Do Extrude Surfaces, Maintain Layers, and Multiple copies is 1. This will copy the circular surface in the positive Z direction and extrude the cylinder at the same time. It will not create the volume. This sequence is illustrated in Figure C2.13. Figure C2.13. Settings for the Copy Control Panel To complete the copy operation Click Select in the Copy menu. The cursor will change to a large square with a small square inside ( ). Select the surfaces of the Circle and quadrilateral. The color will change from magenta to red indicating that GiD has accepted the selection. Click Finish to complete the copy. GiD translated the surface and extruded the cylinder to create a solid model and the corresponding surfaces. This resulting geometry is illustrated Figure C2.14.

10 Figure C2.14. Circle geometry and surfaces copie/extruded The volumes can be added quickly using the menus. The Warning panel confirms the creation of the volumes. This sequence is illustrated in Figure C2.15. Figure C2.17 illustrates the disk after all of the volumes have been created. Click Geometry Create Volume Automatic 6-sided volumes Warning panel with confirmation appears OK Alternative 2: Using the Icons Figure C2.15. Settings for the Copy Control Panel The same process can be accomplished with the icons, however, it requires that all of the bounding surfaces for each volume be selected.

11 Click ( ) Select surfaces that bound the proposed volume Esc to create the volume Esc to quit (When all volumes have been created) See selection of the quadrilateral and the creation of the volume in Figure C2.16. Figure C2.17 illustrates the disk after all of the volumes have been created. Figure C2.16. Selection and creation of Volumes Figure C2.17. Complete Disk Note: If all bounding surfaces are not selected a warning panel appears and the volume is not created. See Figure C2.18. for an example of the warning panel. Figure C2.18. Volume creation error Information window

12 MATERIALS AND CONDITIONS 3. Materials Assignment The next step is to assign the material and boundary conditions necessary for the simulation. Begin by activating ATILA in the Problem type. Click Data Problem type Atila Note: Other compatible versions of Atila may be present, for this example we will use See Figure C2.19. Figure C2.19. Starting ATILA The header will now show the version of Atila being used and the menu and Icons will be available for use, as shown in Figure C2.20. Alternative 1: Using the drop down menu Figure C2.20. ATILA Menus and Icons Click Data Materials Piezoelectric Control Panel appears Select PZT4 Assign by Volumes Select Volumes Finish This sequence is illustrated in Figure C2.21at the top left panel.

13 Alternative 2: Using the Icons Click Control Panel appears Select PZT4 Assign by Volumes Select Volumes Finish. This is illustrated in Figure C2.21 at the top right panel. Top Drop Menu Vertical Icons Bar Figure C2.21. Piezoelectric Material Selection Select all the volumes of the Disk, they will change from cyan to red indicating GiD has accepted the selection. Click Finish or ESC to complete the operation. Click Draw PZT4 to confirm the material has been added. Click Finish or ESC to quit. See Figure C2.22. Figure C2.22. Piezoelectric Material Selection

14 4. Boundary Conditions Assignment Assignment of Boundary conditions is necessary for the simulation. These are the constraints and parameters that will govern how ATILA processes the simulation. This example will cover using the menus and/or the icons. Alternative 1: Using the top drop menus Click Data Conditions as shown in Figure C2.23 left panel. The conditions panel appears as seen in Figure C2.23 bottom panel. Alternative 2: Using the Icons Click ( ) as shown in Figure C2.23, right panel. The conditions panel appears as seen in Figure C2.23 bottom panel. Top Drop Menu Vertical Icons Bar Figure C2.23. Boundary Conditions Assignment 4.2 ASSIGN ELECTRICAL POTENTIAL BOUNDARY CONDITIONS Click Electrical Potential Forced Enter 1.0 Assign Select Surface Finish or Esc.

15 Select Surfaces icon on the top panel and Electrical Potential for the condition. Enter (1.0) in the space provided for the value of the Forced potential. This value is in Volts. After setting the voltage, click Assign and select the top surface of the plate. It will turn red indicating acceptance of the selection. Click Finish to complete. See Figure C1.24. Assign Ground Potential (-) Figure C1.24. Boundary Conditions Control Panel Click Electrical Potential Ground Enter 0.0 Assign Select Surface Select the bottom surface of the bar Finish or Esc. Repeat the same process to assign the Ground electrode. Click Ground Assign, select the bottom surface of the plate. The surface will turn red to signify acceptance of the selection. Click Finish to complete. Confirm the Electrical Potential assignment by clicking Draw Colors. See the result in Figure C.25. Click Finish to quit. Figure C2.25. Electrical Potential assignment confirmation

16 4.3 ASSIGN POLARIZATION BOUNDARY CONDITIONS It is necessary to assign the volume polarization of the piezoelectric material. This will determine the direction of the movement of the material in response to the applied voltage. Click the volume icon ( ) on the top of the control panel, then select Polarization from the list. In this example the default, Cartesian, is selected. Click Define. The Local Axis naming panel will appear as shown in Figure C1.26. It is necessary to name the Local Axis system, for this example use P1. (Note: this can be any name that makes sense or best describes this axis for the particular application.) Enter P1 and press Enter or click OK. Figure C2.26. Boundary Conditions Control Panel - Polarization The orientation dialog window will appear giving two options for defining the axis location and direction. This example will use the X and Angle option. See Figure C1.27. Figure C2.27. Local axis dialog window Note: ATILA Cartesian polarization follows the Z Local direction.

17 There are two options to define the local axis: Alternative 1: Graphical Option Click the X and Angle button and the cursor will change to a plus (+). You will need to select 2 points along the X axis to set the X direction. Right click in the graphics window and click Contextual Join Ctrl-A as shown in Figure C1.28. The cursor will change to a square with the smaller square inside ( ). This change can also be accomplished by holding the Control key and pressing A. Click X and Angle (+) Join Ctrl-a 1 st point Join Ctrl-a 2 nd point Select Angle Assign volumes Finish or ESC. Figure C2.28. Onscreen menu The Join function allows you to select points already created and snap to them. Select the first corner, reselect Join Ctrl-A, select the top corner. See these selections in Figure C2.29. left panel. A moveable axis will appear, move the mouse to orient it in the desired direction, for this example match the graphic Z axis or 180 degrees. The angle will appear next to the cursor, when it is at 180 click the Right Mouse Button to select. See illustration in Figure C2.29 left panel, red circle. The polarization axis is shown in Figure C2.29. right panel. 1 2 Figure C2.29. Creation of Local axis

18 Alternative 2: Coordinate Entry Option Click X and Angle Enter axis center Enter Enter point in positive X direction Enter Enter Angle for Y Assign volumes Finish or ESC. Click the X and Angle button and the cursor will change to a plus (+). Move the cursor to the Command Line, enter the coordinates for the Center of the local axis, Enter. Enter the coordinates for a point in the positive X direction Enter. Enter the Angle to define the Y axis (This is relative to the graphic axis). These steps are shown in Figure C2.30. The Polarization axis will appear as shown in Figure C2.29. right panel. Figure C2.30. Boundary Conditions Control Panel To confirm the assignment of polarization click Draw All conditions Include local axis. The process and results are shown in Figure C2.31. Figure C2.31. Confirmation of Polariation Note: All of the conditions will be shown in red. See center panel of Figure C2.31. Select Finish or ESC to quit Draw.

19 MESH 5. Meshing the model The geometry is created, the material assigned, and the conditions assigned, the next step is to mesh the model. Meshing divides the part into geometric components that the software uses to calculate the stress, deformation, etc to create the outputs used for analysis. There are several options to generate the mesh. Here we provide two examples. More details can be found in GiD help. 5.1 SETTING MESH TYPE The default mesh type in GID is Normal, this example will use Quadratic. Note: Changes made in the preferences will remain until changed or the preferences reset to the default settings. Alternative 1: Change mesh type Menu option Click Utilities Preferences Preference Control Panel appears Meshing Quadratic Accept Close The menu is shown in Figure C2.32, the Preference Control Panel is shown in Figure C2.33. Figure C2.32. Menu selection for Preferences Alternative 2: Change mesh type Hot Key option CTRL + P Preference Control Panel appears Meshing Quadratic Accept Close The Preference Control Panel is shown in Figure C2.33.

20 Figure C2.33. Preferences Control Panel 5.2 STRUCTURED MESH To setup the structured mesh follow these steps as illustrated in Figure C2.34. Click Mesh Structured Volumes Assign number of cells Figure C2.34. Creating a Structured Mesh The cursor will change to a square with the small square in the center ( ), select the volume you want to mesh. Press ESC. (Note: This process will be followed for each volume to be meshed if there is more than one. The mesh of adjacent volumes must be the same size.). This example will mesh all of the volumes with the same size elements. The control panel shown in Figure C2.35., left panel, will appear. Enter the number of divisions for a line. Click Assign.

21 Figure C2.35. Assigning number of divisions. Select the 6 divisions for the radial lines and the circunference lines. The cursor will change ( ) to allow the selection of the lines for that number of divisions. When the lines are selected they will turn red indicating acceptance. (Note: Depending on the method of construction lines that are opposite one another will all be selected together, this is the case in this example. See Figure C2.36. right panel) When finished selecting the lines for that number of divisions press ESC. The Control Panel will reappear with the option to enter a different value as shown in Figure C2.36., left panel. The selection process is the same as used in the previous step. When all of the lines have been assigned a number of divisions press ESC, then ESC again to quit. Figure C2.36. Assigning number of divisions for the plate thickness. Press CTRL + G, the Mesh Generation control panel below will appear. Click Get meshing parameters from model and click OK, see Figure C2.37. left panel. The mesh will be generated, select View mesh to see the mesh as illustrated in Figure C2.38 panel. Figure C2.37. Meshing the geometry

22 Figure C2.38. Meshing the geometry. Left: using hexahedra elements; Right: using tetahedra elements. Note: In GiD 10, the default element type is hexahedra, so the resulting meshing will be the one shown in Figure C2.38 left. Howeever, in GiD 11, the default element type is tetahedra and the results of using CTR + G will be as shown in Figure C2.38 right. Hexahedra elements uses less numbers of nodes than when using tetaedra elements. To select hexahedra as the element for the mesh, select Mesh Element Type Hexahedra. This can be observed in Figure C2.39 Figure C2.39. Selection of Hexahedra elements fot the meshing.

23 CALCULATE 6. Calculations The model has been created, the material and the boundary conditions assigned, and the geometry Meshed, the next step is to assign the Problem Data. The Problem Data menu assigns the rules for the simulation. These rules determine the type of simulation, the number of steps, etc that are to be run to generate the data for analysis. 6.1 HARMONIC CALCULATION STEP 1: SELECT HARMONIC ANALYSIS FROM PROBLEM DATA Click Data Problem Data, the Control Panel will appear. (alternatively, click ) Click Geometry 3D. Click Analysis Harmonic. Click Include Losses Write strain Write stress Accept. The lower left corner of the control panel will flash the message Problem Data modified. See these steps in Figure C2.40. Figure C2.40. Assign Problem Data STEP 2: ENTER THE FREQUENCY RANGE TO PERFORM THE HARMONIC ANALYSIS Click Data Interval Data. The Interval Data Control Panel will appear. (alternatively, click ) Click TYPE LINEAR DISTRIBUTION. Enter the Minimum and Maximum frequencies and the number of frequencies to be tested. (Note: More points tested will give a smoother Admittance/Impedance graph and more accurate results. However the calculation time will increase correspondingly.) Click Accept when finished, the lower left corner of the control panel will flash the message Interval Data modified. The sequence is shown in Figure C2.41.

24 Figure C2.41. Assign Interval Data At this point, all of the necessary information to perform an harmonic calculation has been entered. The next step is to run the calculation/simulation. STEP 3: START THE CALCULATION Click Calculate Calculate as shown in Figure C2.42 left panel. The calculation dialog box will appear briefly letting you know the calculation has started. See Figure C2.42 center panel. Note: The progress can be monitored by clicking Calculate, then View Process info This will open the window displaying the calculation processes as they are proceeding. When the calculations are complete the Process Info panel will appear. Click Post-process to open the postprocessor and view the results of the simulation. See Figure C2.42 right panel. Figure C2.42. Calculation Panels

25 RESULTS 7. Post-Process/View Results The post-process mode will appear similar to the preprocess mode with the addition of several new commands and icons. See window in Figure C2.43. On the left, select the Display Style icon to change the style of visualization. In Figure C2.43, the display style has been selected to activate the mesh. Figure C2.43. Post-Processor Window TIP: To enter to the postprocessor mode after exiting or for a calculation that has been run previously, open the file and click ( ). This will load the data and open the postprocessor window. 7.1 ADMITTANCE GRAPH Click ( ) Admittance: Magnitude Results Select Admittance Select View Graph. The Admittance & Impedance Results control panel will appear, as seen in Figure C2.43. Figure C2.43. Admittance/Impedance Control Panel Select the desired characteristic, Admittance: Magnitude, then select View Graph. The Admittance magnitude graph will appear as seen in Figure C2.44.

26 The Admittance magnitude graph will appear, see Figure C1.36. left panel. Other options available include Phase, Conductance, Susceptance and Circle admittance and associated values for the Impedance as illustrated in Figure C2.44. To get the exact coordinates of a point on the graph right click in the graphics window. The contextual menu will appear, select Label Select Res, as seen in Figure C2.44 for the maximum value of the admittance plot. Figure C2.44. Admittance Magnitude Graph The values of the graph can be exported to an Excel file for later analysis. In order to do so, select the ATILA menu and then Open shell. The file named with the problem_name.adm.csv includes the admittance data. The file named problem_name.imp.csv includes the impedance data. This is illustrated in Figure C2.45. Figure C2.45. The impedance and admittance data can be open in Excel format.

27 A clearer picture of the admittance graph can be seen by transforming the Y scale of the graph to a log scale. To make this change click Options Graphs Y axis Set Logarithmic Scale. The confirmation window will appear, click Yes. See Figure C2.46. for this process. Figure C2.46. Converting Y axis to Log10 Scale The graph now displays the result with a log scale. The resonant peaks can be seen more clearly as shown in Figure C2.47. Figure C2.47. Admittance Graph To remove the admittance graphs select the clear graphs icon ( ).

28 7.2 VIEW RESULTS - DEFORMED SHAPE In addition to generate the admittance and impedance values, ATILA provides different type of results for the harmonic simulation. Select View results or select the icon vertical menu to select one of the visualization modes for the results as shown in Figure C Drop Menu Vertical Icons Menu Contour Fill Contour Lines Show Min Max Display Vectors Iso Surfaces Stream Lines Result Surface Deformation Figure C2.48. View Results display options. For an harmonic simulation, the results are provided for each frequency. Let's select the frequency of Hz corresponding to the maximum of admittance and let's display the Total displacement using the Contour Fill visualization. First select the desired frequency using View Results Default Analysis/Step. Then, it is possible to select the Imag Part, the Magnitude or the Real Part for the results. We will choose Magnitude for this example and then we pick up as shown in Figure C2.49. Figure C2.49. Selection of the specific frequency to show the results.

29 Next, we select Contour Fill Displacement Total Displacement as shown in Figure C Figure C2.50. Selection of Total Displacement using Contour Fill visualization option. This will retrieve the total displacement in the disc, which in this case correspond to the radial vibration for the first resonance mode as shown in 7.3 ANIMATION Figure C2.51. Total Displacement in the disc for the frequency of 46000Hz. To run the animation follow the steps below. 1. Select the frequency to view: Click View Results Default Analysis/Step Harmonic-Magnitude Value (for instance Hz) 2. Load the animation: Click ( ) Atila Animation window appears Click OK The Atila Animation panel illustrated in Figure C2.52 confirms the frequency selected and activates the loading process for the animation. Figure C2.52. Animation panel.

30 Inmediatly after this, the ATILA Animate window will appear. This window allows the user to play the movie, save the movie, etc. The ATILA Animate window is shown in Figure C2.53. Figure C2.53. ATILA Animate window. 3. Select Deformed shape Once the Animation Control panel has appeared, click ( ) and select a deformation magnitude factor to show the deformed shape. The factor can be adjusted progressively to obtain the best representation of the results. 4. Run the animation Click ( ) to run the animation, the panels in Figure C2.54. illustrate the animation results at the maximum and minimum harmonic positions. As explained in Case 1 the animation can be stopped at any point by clicking ( ) and stepped through each modal point by clicking ( ) or moving the ( ). Figure C2.54. Different steps observed during the animation.

31 5. Add visualization options to show specific results: EXAMPLE: Total Displacement The animation can be stopped and other conditions added to the visualization, such as the displacement. Note: To add or change the visualization the animation must be stopped and restarted after the changes are made. In this example the Total-Displacement will be displayed in the animation. Alternative 1: View Total Displacement using the menus Click View Results Contour Fill Displacement X-Displacement Alternative 2: View X-Displacement using the icons Click ( ) Displacement X-displacement OR Figure C2.55. Steps to view X-Displacement The average displacement is shown in the lower right corner of the graphics window, the value is keyed to the corresponding color on the part as illustrated below in Figure C2.56. Figure C2.56. Animation of the total displacement for 46,000 Hz

32 EXAMPLE: Stress Sxy Alternative 1: View Stress Sxy using the menus Click View Results Contour Fill Stress Sxy Alternative 2: View Stress Sxy using the icons Click ( ) Stress Sxy OR Figure C2.57. Steps to visualize Stress on Part Figure C2.58. illustrates the results of stress visualization as seen in Atila/GID Figure C2.58. Animation of the Sxy for 46,000 Hz.